Noncommutative function theory and unique extensions

• Autorzy: David P. Blecher , Louis E. Labuschagne
• Języki publikacji: EN

Abstrakty

EN

We generalize, to the setting of Arveson's maximal subdiagonal subalgebras of finite von Neumann algebras, the Szegő $L^{p}$-distance estimate and classical theorems of F. and M. Riesz, Gleason and Whitney, and Kolmogorov. As a byproduct, this completes the noncommutative analog of the famous cycle of theorems characterizing the function algebraic generalizations of $H^{∞}$ from the 1960's. A sample of our other results: we prove a Kaplansky density result for a large class of these algebras, and give a necessary condition for every completely contractive homomorphism on a unital subalgebra of a C*-algebra to have a unique completely positive extension.

Kategorie tematyczne

• 47L75: Other nonselfadjoint operator algebras
• 46L52: Noncommutative function spaces
• 47L45: Dual algebras; weakly closed singly generated operator algebras
• 46L51: Noncommutative measure and integration
• 46K50: Nonselfadjoint (sub)algebras in algebras with involution
• 46J15: Banach algebras of differentiable or analytic functions, H p -spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2007
• Tom: 178
• Numer: 2
• Strony: 177-195

Daty

wydano

2007

Twórcy

autor

David P. Blecher

• Department of Mathematics, University of Houston, Houston, TX 77204-3008, U.S.A.

autor

Louis E. Labuschagne

• Department of Mathematical Sciences, P.O. Box 392, 0003 Unisa, South Africa

Identyfikatory

DOI

10.4064/sm178-2-4